I am running regressions where I need to compare the coefficients with the base, but I am a little confused about how to introduce the control variables.
My regression looks as per:
log(wage) = B + B(black) + B(Hispanic) + B(black*noeducation) + B(Black*Highschool) + B(Black*College) + B(Hispanic*noeducation) + B(Hispanic*Highschool) +B(Hispanic*College) + B(2002) + B(2003) + B(2004) + B(education) + B(office) + B(Highschool) + B(College)
This is whereby my data set has the following variables:
Race variables : Black, Hispanic, White
Education variables: no education, High School, College
Year variables: 2001, 2002, 2003, 2004
Occupation variables: education, medical, office
The coefficients of interest are B(Hispanic$*$noeducation) and B(Black$*$noeducation) because I want to see if there is a difference for returns on wages for black people and hispanic people with no education compared to white people with no education. However, I am scared about my controls affecting it because technically won't these coefficients tell me the difference of return on wages of black people and hispanic people compared to white people in 2001, in the medical sector with no education. If this is correct, how would I overcome this to just compare regardless of year and occupation variables?